Fractional Helmholtz operators admit high-frequency geometrical optics solutions, and for s≥1/2 these give Hölder stable recovery of the potential from multi-frequency boundary Cauchy data.
On an inverse problem for a fractional semilinear elliptic equation involving a magnetic potential
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We study a class of fractional semilinear elliptic equations and formulate the corresponding Calder\'on problem. We determine the nonlinearity from the exterior partial measurements of the Dirichlet-to-Neumann map by using first order linearization and the Runge approximation property.
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Geometrical optics for the fractional Helmholtz equation and applications to inverse problems
Fractional Helmholtz operators admit high-frequency geometrical optics solutions, and for s≥1/2 these give Hölder stable recovery of the potential from multi-frequency boundary Cauchy data.